
In Bayesian hypothesis testing formulation, the detector knows the probabilities that \(H_1,H_0\)  hold true are \(c_1,\;c_0\)  (\(c_1 + c_0 = 1\) ) respectively. Referring to [1]} and denoting \(\tau = \frac{c_1}{c_0}\) , detector's optimal solution measurement \(\Pi ^*_1\)  can be designed as follows:
\(\Pi ^*_1(\tau ) = \sum _{\eta _j>0}{|\eta _j\rangle \langle \eta _j|},\) 
